Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 32π at its centre is:
Solutions · 1
Official solution
Let \[M\left( {h,k} \right)\] be the mid point of chord AB where
\[\angle AOB = {{2\pi } \over 3}\]
\[\therefore\] \[\angle AOM = {\pi \over 3}.\] Also OM= \[3\cos {\pi \over 3} = {3 \over 2}\]
\[ \Rightarrow \sqrt {{h^2} + k{}^2} = {3 \over 2}\]
\[ \Rightarrow {h^2} + {k^2} = {9 \over 4}\]
\[\therefore\] Locus of \[\left( {h,k} \right)\] is
\[{x^2} + {y^2} = {9 \over 4}\]